Road surface friction and surface type estimation system and method

ABSTRACT

A tire-based system and method for estimating road surface friction includes a model-based longitudinal stiffness estimation generator using tire-based parameter inputs and vehicle-based parameter inputs; an actual longitudinal stiffness estimation generator using real-time vehicle-based parameter inputs; and a tire road friction estimation generator for deriving a tire road friction estimation from a comparative analysis between the actual longitudinal stiffness estimation and the model-based longitudinal stiffness estimation. A road surface classifier algorithm is employed to generate a road surface type analysis from the road friction estimation, an ambient air temperature measurement, and an ambient air moisture measurement.

FIELD OF THE INVENTION

The subject invention relates generally to systems for estimating a roadsurface condition and, more specifically, to a tire based road surfacecondition friction estimation system and method.

BACKGROUND OF THE INVENTION

Real-time measurement or estimation of road surface condition areimportant and useful to vehicle control systems such as adaptive cruisecontrol (ACC), anti-lock braking systems (ABS), electronic stabilityprogram (ESP) and acceleration slip regulation (ASR). Reliable andaccurate road surface condition information is important for suchsystems to function as intended. Typical road surface evaluation systemsattempt to estimate road friction coefficients through estimationschemes that require certain levels of vehicle longitudinal and/orlateral motion excitations (e.g. accelerating, decelerating andsteering) and a persistence of such excitation levels in order toachieve a reliable friction estimation. While such schemes are valid intheory, attaining the requisite level and persistence of excitation toachieve a reliable friction estimation, however, has proven problematicin practice.

Accordingly, an improved reliable and robust system and method forestimating road surface friction is desired for use in advanced vehiclecontrol systems.

SUMMARY OF THE INVENTION

A tire-based system and method for estimating road surface frictionincludes a model-based longitudinal stiffness estimation generatoroperable to generate a longitudinal stiffness estimate from tire-basedparameter inputs and vehicle-based parameter inputs; an actuallongitudinal stiffness estimation generator operable to generate anactual real-time longitudinal stiffness estimate from vehicle-basedparameter inputs; and a tire road friction estimation generator forderiving a tire road friction estimation from a comparative analysisbetween the actual longitudinal stiffness estimation and the model-basedlongitudinal stiffness estimation.

In a further aspect of the invention, the tire-based parameter inputsare one or more parameter inputs taken from the group: tireidentification; tire temperature, and tire air cavity pressure which areused as adaption factors within a model-based longitudinal stiffnessestimation algorithm. The vehicle-based parameter inputs are one or moreparameter inputs from the group wheel speed of the vehicle, wheeltorque, wheel hub vertical acceleration and wheel slip ratio. Thevehicle-based parameter inputs are used in the actual real-timelongitudinal stiffness estimation.

In yet another aspect, the system and method uses a tire wear stateestimation from the measured hub vertical acceleration. The model-basedlongitudinal stiffness estimation generator generates a longitudinalstiffness estimation from vehicle load, the tire air cavity pressure,and the tire temperature compensated by the estimated tire wear state.

A longitudinal force estimation generator, as a further aspect of theinvention, is deployed for estimating longitudinal force from themeasured wheel speed and the measured wheel torque. A longitudinalstiffness generator estimates the actual longitudinal stiffness from theestimated longitudinal force and a measured wheel slip ratio.

According to yet another aspect, the system includes a road surfaceclassifier algorithm generating a road surface type analysis from theroad friction estimation, an ambient air temperature measurement, and anambient air moisture measurement.

DEFINITIONS

“ANN” or “Artificial Neural Network” is an adaptive tool for non-linearstatistical data modeling that changes its structure based on externalor internal information that flows through a network during a learningphase. ANN neural networks are non-linear statistical data modelingtools used to model complex relationships between inputs and outputs orto find patterns in data.

“Aspect ratio” of the tire means the ratio of its section height (SH) toits section width (SW) multiplied by 100 percent for expression as apercentage.

“Asymmetric tread” means a tread that has a tread pattern notsymmetrical about the center plane or equatorial plane EP of the tire.

“Axial” and “axially” means lines or directions that are parallel to theaxis of rotation of the tire.

“CAN bus” or “controller area network” is a vehicle bus standarddesigned to allow microcontrollers and devices to communicate with eachother within a vehicle without a host computer. CAN bus is amessage-based protocol, designed specifically for automotiveapplications.

“Chafer” is a narrow strip of material placed around the outside of atire bead to protect the cord plies from wearing and cutting against therim and distribute the flexing above the rim.

“Circumferential” means lines or directions extending along theperimeter of the surface of the annular tread perpendicular to the axialdirection.

“Equatorial Centerplane (CP)” means the plane perpendicular to thetire's axis of rotation and passing through the center of the tread.

“Footprint” means the contact patch or area of contact created by thetire tread with a flat surface as the tire rotates or rolls.

“Groove” means an elongated void area in a tire wall that may extendcircumferentially or laterally about the tire wall. The “groove width”is equal to its average width over its length. A grooves is sized toaccommodate an air tube as described.

“Inboard side” means the side of the tire nearest the vehicle when thetire is mounted on a wheel and the wheel is mounted on the vehicle.

“Kalman Filter” is a set of mathematical equations that implement apredictor-corrector type estimator that is optimal in the sense that itminimizes the estimated error covariance when some presumed conditionsare met.

“Lateral” means an axial direction.

“Lateral edges” means a line tangent to the axially outermost treadcontact patch or footprint as measured under normal load and tireinflation, the lines being parallel to the equatorial centerplane.

“Luenberger Observer” is a state observer or estimation model. A “stateobserver” is a system that provide an estimate of the internal state ofa given real system, from measurements of the input and output of thereal system. It is typically computer-implemented, and provides thebasis of many practical applications.

“Net contact area” means the total area of ground contacting treadelements between the lateral edges around the entire circumference ofthe tread divided by the gross area of the entire tread between thelateral edges.

“Non-directional tread” means a tread that has no preferred direction offorward travel and is not required to be positioned on a vehicle in aspecific wheel position or positions to ensure that the tread pattern isaligned with the preferred direction of travel. Conversely, adirectional tread pattern has a preferred direction of travel requiringspecific wheel positioning.

“Outboard side” means the side of the tire farthest away from thevehicle when the tire is mounted on a wheel and the wheel is mounted onthe vehicle.

“Peristaltic” means operating by means of wave-like contractions thatpropel contained matter, such as air, along tubular pathways.

“Piezoelectric Film Sensor” a device in the form of a film body thatuses the piezoelectric effect actuated by a bending of the film body tomeasure pressure, acceleration, strain or force by converting them to anelectrical charge.

“Radial” and “radially” means directions radially toward or away fromthe axis of rotation of the tire.

“Recursive least squares (RLS)” means an adaptive filter algorithm whichrecursively finds the filter coefficients that minimize a weightedlinear least squares cost function relating to the input signals.

“Rib” means a circumferentially extending strip of rubber on the treadwhich is defined by at least one circumferential groove and either asecond such groove or a lateral edge, the strip being laterallyundivided by full-depth grooves.

“Sipe” means small slots molded into the tread elements of the tire thatsubdivide the tread surface and improve traction, sipes are generallynarrow in width and close in the tires footprint as opposed to groovesthat remain open in the tire's footprint.

“Slip Angle” is the angle between a vehicle's direction of ravel and thedirection in which the front wheels are pointing. Slip angle is ameasurement of the deviation between the plane of tire rotation and thedirection of travel of a tire.

“Tread element” or “traction element” means a rib or a block elementdefined by having a shape adjacent grooves.

“Tread Arc Width” means the arc length of the tread as measured betweenthe lateral edges of the tread.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described by way of example and with reference tothe accompanying drawings in which:

FIG. 1 is a graph showing tire longitudinal stiffness vs. wheel slipratio for four types of road surface conditions.

FIG. 2 is a graph of tire longitudinal stiffness vs. wheel slip ratio inthe small-slip region of the graph of FIG. 1.

FIGS. 3A through 3D are force-slip curve comparison graphs comparingnormal to cold tires; new to worn tires, high inflated to low inflatedtires and summer to all season tires, respectively.

FIG. 4 is a table summarizing road friction dependency for four tiresunder dry braking and wet braking conditions.

FIG. 5A is a graph showing lad and pressure dependency and a load andpressure adaption algorithm adjusting for the dependency in longitudinalstiffness calculation.

FIG. 5B is a test result graph showing load-pressure-wear dependency at60 mph for new and worn tires at different inflation pressures. Thegraph shows braking stiffness vs. load and provides a wear adaptionalgorithm adjusting for the wear dependency in a stiffness calculation.

FIG. 5C is a graph showing dependency of braking stiffness to load andtemperature and representing an expression adapting stiffness totemperature.

FIG. 5D is a representation of the expressions for load and pressureadaptation, temperature adaptation and wear adaptation and their use asscaling expressions in a model based longitudinal (stiffness)estimation.

FIG. 6 is a schematic representation of the friction estimate system andmethod.

FIG. 7 is an on-vehicle implementation flowchart of the frictionestimate system and method showing the integration of actual andmodel-based stiffness calculations in the tire road friction estimate.

FIGS. 8A through 8C are validation graphs showing SMC Observer Basedlongitudinal force estimation over time in a test sequence vs. actual.

FIG. 9A is a graph showing validation of on-vehicle estimation of tireslip ratio over time.

FIG. 9B is a graph showing tire road friction coefficient estimationover time.

FIG. 9C shows a graph of algorithm activation signal.

FIG. 9D shows a graph of estimation results of longitudinal stiffnessover time.

FIG. 10A is a flow chart of the use of friction estimation and airtemperature and moisture inputs into a detailed road surface classifier.

FIG. 10B is a table showing the classes of road surface.

FIG. 11 is a graph of road surface classifier performance showing actualvs. predicted (with and without wear state adaptation) frictionestimation comparison and showing the resultant misclassification(without tire wear compensation).

FIG. 12 is a graph of road surface classifier performance showing actualvs. predicted (with and without temperature state adaption) frictionestimation comparison and showing the resultant misclassification(without temperature compensation).

DETAILED DESCRIPTION OF THE INVENTION

Accurate estimation of tire-road friction has utility in theimplementation of vehicle control systems. Estimation methods can becategorized into “cause-based” and “effect-based” approaches accordingto the fundamental phenomena. “Cause-based” strategies try to measurefactors that lead to changes in friction and then attempt to predictwhat friction change will be based on past experience or frictionmodels. “Effect-based approaches, on the other hand, measure the effectsthat friction has on the vehicle or tires during driving. They attemptto extrapolate what the limit friction will be based on this data.

The measurement of vehicle motion itself may be used to obtain anestimate of the tire-road friction coefficient. Two types of systems maybe employed: systems that utilize longitudinal vehicle dynamics andlongitudinal motion measurements and systems that utilize lateralvehicle dynamics and lateral motion measurements. The lateral system canbe utilized primarily while the vehicle is being steered while alongitudinal motion-based system is applicable generally during vehicleacceleration and deceleration.

An approach to assess the friction of a road-surface is to estimate thelongitudinal stiffness, i.e. the incline of the tire force relative toslip and from this value distinguish between different surfaceconditions. FIG. 1 shows a graph of longitudinal stiffness F_(x)[N] vs.wheel slip ratio [λ] for different road surface conditions. FIG. 2 showsan enlarged low slip region of the graph of FIG. 1. As will be noted,the incline of the tire force relative to slip at low slip regions ofthe curves makes deriving a maximum friction coefficient problematicfrom the value of slip-slope alone. The subject invention thereforepresents a system and method of estimating the friction coefficientusing the slip-slope method but adapts a slip-slope approach toincorporate important parameters that govern tire longitudinal stiffnessbehavior in the low slip region. Parameters included in the estimationadaptation include tire inflation pressure, tread depth (tire wearcondition), normal loading, tire construction, and temperature. Suchparameters are measured from tire-based sensors and are used tocompensate for dependencies of pressure, temperature, wear state, tireconstruction on friction estimation.

FIGS. 3A through 3D demonstrate how significant such tire-basedparameters are to a determination of longitudinal force in the low slipregion of the curves. The graph of FIG. 3 validates that tiretemperature affects the force-slip curve, comparing the curves of anormal tire 1 at 30° C. to a cold tire 2 at 0° C. FIG. 3B shows tirewear dependency in comparing new tire tread depth to a worn tire treaddepth. FIG. 3C shows the force-slip curve comparison between a highinflation pressure tire at 41 psi and a low inflation pressure tire at22 psi. FIG. 3D confirms the dependency of the force-slip curve in a lowslip region on tire construction, comparing a Goodyear Eagle F1 tire toan All-Season Eagle tire. A summary of the test results comparing thetires is presented in tabular form in FIG. 4. As will be seen, thepercentage change between wet braking and dry braking is significant andvaries between tires of differing construction.

The following generalizations may be drawn from the test resultsreflected in FIGS. 3A through 3D. As compared to a normal tire at 30°C., the cold tire has 40 to 45 percent higher braking stiffness. Ascompared to a tire at a higher pressure, the tire at a lower pressurehas a slightly lower braking stiffness. As compared to a new tire, theworn tire has 30 percent higher braking stiffness. As compared to asummer tire, an all season tire has a dramatic effect on the brakingstiffness. Finally, as summarized in FIG. 4, there is noted a 15 percentdrop in stiffness during wet conditions. The load on a tire thus has amoderate effect on longitudinal stiffness (C_(x)), about 10 percent per100 pounds; tire inflation pressure has a relatively small dependence;tire wear state has a high dependency, about 30 percent in new vs. worn;tire temperature has a high dependency, about 45 to 50 percent in a coldtire vs. normal temperature tire; and road surface type (friction) has ahigh dependency, about 10 to 15 percent in dry vs. wet and 90 percent indry vs. ice. The conclusion to be drawn is that a tire's slip slope isdifferent based on the factors above. Thus, the subject system andmethodology does not use only the value of the slip slope itself but,rather, employs factor adaptation models to compensate for the inflationpressure, tread depth, normal loading and temperature dependencies.

FIGS. 5A through 5C shows the adaptation and compensation models forload and pressure, wear, temperature. In FIG. 5A. adaptation model forSL attributed to load and pressure is shown by first order in pressureand second order in load components, in which:

SL=load and pressure adaptation factor

Fz=load

Fzo=nominal load

P=pres sure

P_(o)=nominal pressure

q_(f)=model scaling coefficients for load

q_(p)=model scaling coefficients for pressure

Wear adaptation is represented in the expression for SW shown in FIG. 5Bin which:

SL=wear state adaptation factor

W=tread depth

W_(o)=nominal tread depth

q_(w)=model scaling coefficients for the tire wear state

In FIG. 5C the braking stiffness adaptation model is indicated by theexpression for ST in which:

ST=temperature adaptation factor

T=tire temperature

T_(o)=nominal tire temperature

q_(t)=model scaling coefficients for tire temperature

The load, pressure, wear, and temperature adaptations embodied withinthe model expressions of FIGS. 5A through 5C are integrated into thescaled stiffness under actual operating conditions C_(x) model shown inFIG. 5D. FIG. 6 is a schematic representation of the friction estimatesystem and method. Referring to FIG. 6, tire-based model inputs 10consist of tire ID (used to identify tire type and construction),pressure and temperature are obtained from sensors within atire-attached TPMS module. One or more TPMS modules are mounted to eachtire 12 supporting vehicle 14. The TPMS modules (not shown) may bemounted to an inner liner of the tires by conventional means such as anadhesive. Each TPMS module through commercially available sensorsmonitors tire pressure and temperature and contains stored dataidentifying the tire. The data from each TPMS module may be transmittedwirelessly to a data processor for stiffness estimation. In addition,further tire-based inputs 10 into the adaptation model for deriving aModel-based Longitudinal Stiffness Estimation 16 include tire wear stateand tire load, available from tire-based sensors or indirectly fromvehicle based sensors.

An Actual Longitudinal Stiffness Estimation 20 is determined from aforce slip observer and is affected by load, pressure, temperature, wearstate and tire-road friction. The Actual Longitudinal StiffnessEstimation 20 is derived from vehicle-based inputs available sensors oncommercially available vehicles. The vehicle-based Actual LongitudinalStiffness Estimation 20 and the model-based Longitudinal StiffnessEstimation 16 are used in the algorithm 18 which conducts a recursiveleast square estimation with forgetting factor analysis and outputs thetire road friction estimate 22 sought. The friction scaling factor usedin the RLS Estimation With Forgetting Factor is a direct measure of thetire road friction coefficient. It will be appreciated that the ActualLongitudinal Stiffness Estimation 20 utilizes a force slip observer. TheModel-based Longitudinal Stiffness Estimate 16 employs the algorithmidentified and considers dry road condition as the reference condition.

The on-vehicle implementation flowchart of the FIG. 6 system and methodis shown in FIG. 7. As explained, the vehicle 14 is shown as a passengercar but may be any type of vehicle carried by tires 12. Tires 12 areeach equipped with a mounted TPMS module (not shown) from which inputs44 (tire ID, pressure, temperature) from each tire are sensor generated.The vehicle 14 is equipped with a CAN Bus (controller area network) andon-vehicle sensors that generate measurement of hub verticalacceleration 26, slip ratio 34, wheel speed and torque 28, andmeasurement of vehicle load 42. The wheel speed and torque 28 are usedto produce a longitudinal force estimation F_(x) 42 using a sliding modeobserver (SMC). The longitudinal force estimation F_(x) 42 is input withthe slip ratio 34 into a longitudinal stiffness estimation model 20 thatutilizes a recursive least square (RLS) with forgetting factoralgorithm. From the longitudinal stiffness estimator 20 a longitudinalstiffness (actual) computation 36 is made.

The model-based longitudinal estimation 46 proceeds as follows. Fromon-board vehicle sensors a hub vertical acceleration is accessed fromCAN bus 24. The hub vertical acceleration 26 is input into a tire wearstate estimator. Such an estimator system and method is disclosed inpending U.S. patent application Ser. No. 13/917,691 filed Jun. 14, 2013,hereby incorporated by reference herein. From estimator 38, a wear stateestimation 40 is made and used as an input with a vehicle-basedmeasurement of vehicle load 42 into the model based longitudinalstiffness estimation 46. Tire-based inputs 44 are likewise input intothe estimation 46, the inputs 44 including a tire ID (used to identifytire-specific structural composition), tire cavity pressure and tireliner temperature. The vehicle-based inputs of wear state 40 and load42, together with tire-based inputs 44 of tire ID, pressure andtemperature, are applied within the adaptation model 16 described abovein regard to FIG. 6. Coefficients in the expression in FIG. 6 are tirespecific. A tire specific empirically generated database is constructedfor each tire using the subject system. Once the tire ID is determined,it is used to consult the database and retrieve tire specificcoefficients to be used in the model-based calculation of C_(x). Theload scaling, pressure scaling wear state scaling, and temperaturescaling components to algorithm 16 yield an acceptably accuratecompensated model-based estimation of the longitudinal stiffness C_(x)48.

The model is given in FIG. 7 at numeral 16 wherein:

C_(o)=Stiffness under nominal operating conditions,

C_(x)=Scaled stiffness under actual operating conditions.

The compensated model-based longitudinal stiffness estimate C_(x) isinput with the longitudinal stiffness (actual) measurement 20 based onactual vehicle-based inputs of force (F_(x)) and slip ratio (λ) into aRecursive Least Square Estimation With Forgetting Factor Algorithm 18 asshown. The longitudinal stiffness (actual) from vehicle-based sensors iscompared with the longitudinal stiffness estimation 48 (modelbased-load, pressure, temperature, wear compensated) and the differencebetween the two longitudinal stiffness estimations attributed to tireroad friction 22. The estimation of tire road friction 22 thus utilizesboth a model-based tire-input compensated longitudinal stiffnessestimation and a vehicle-based estimation of longitudinal stiffness toachieve a more accurate estimation.

The on-vehicle estimation of tire longitudinal force (F_(x)) is achievedby an estimation algorithm derived as follows. The dynamic equation ofthe angular motion of a wheel is give as:

Jω _(w)=(T _(w) −T _(b))−F _(x) r _(w) −F _(rr) r _(w)

J:wheel inertia

ω_(w):wheel speed

T_(w)=drive torque.

T_(w):brake torque

F_(x):longitudinal force

r_(w):tire rolling radius

F_(rr):tire rolling resistance force

Where the subscripts have been omitted for convenience. The sameestimator and equations hold for all the wheels. Rearranging Equation(3.14) yields an expression for the longitudinal force as:

$F_{x} = {\frac{\left( {T_{w} - T_{b}} \right) - {J\; \omega_{w}^{\prime}}}{r_{w}} - F_{rr}}$

Here, the wheel drive torque can be estimated by using the turbinetorque, the turbine angular velocity, and the wheel angular velocity. Itis assumed that the brake pressure of each wheel is an available signal.Therefore, the brake torque can be computed by the brake gain. The wheelrolling resistance force is given by the expression:

F _(rr)=0.005+324·0.01·(r _(w)·ω_(w))²

The accuracy of longitudinal force estimation using the above equationdepends on the accuracy of the effective tire radius. Obtaining anaccurate estimate of effective tire radius may be determined as:

$r_{w,i} = {r_{o} - \frac{F_{z,i}}{k_{t}}}$

r_(o):rolling radius at nominal load

r_(w,i):rolling radius at operating load

F_(z,i):operating tire load

k_(t):tire vertical stiffness

Even though the above equation is a relatively simple (open-loop) methodto estimate the longitudinal tire force F_(x) (i.e. the longitudinalforce may be calculated directly using the equation 3.15, or by use of arecursive least squares (RLS) method for a smoother estimation), findingthe time derivative of angular wheel speed signals in real-worldconditions can pose challenges. To avoid the need to take thederivatives of angular wheel speed signals, a sliding mode observer(SMO) based estimation scheme may be used. The SMO uses a sliding modestructure, with the state estimate evolving according to the wheeldynamics model (ref. Eq. (3.14)), the force model, and the sign of themeasurement estimation error.

J{circumflex over ({dot over (ω)}_(w)=(T _(w) −T _(b))−{circumflex over(F)} _(x) r _(w) −F _(rr) r _(w) +k ₁ sgn(ω_(w)−{circumflex over(ω)}_(w))

{circumflex over (F)}x=k ₂ sgn(ω_(w)−{circumflex over (ω)}_(w))

Here k₁ & k₂ are the observer gains and sgn(.) denotes signum functiondefined as:

${{sgn}\left( {s(t)} \right)} = \left\{ \begin{matrix}{1,{{{if}\mspace{14mu} {s(t)}} > 0}} \\{0,{{{if}\mspace{14mu} {s(t)}} = 0}} \\{{- 1},{{{if}\mspace{14mu} {s(t)}} < 0}}\end{matrix} \right.$

A validation of the subject system and method was conducted and theresults are reflected in the graphs of FIGS. 8A, 8B, 8C. The proposedSMC based longitudinal force estimation algorithm was evaluated insimulations by implementing it in CARSIM, an industry standard vehicledynamics simulation software. The vehicle maneuver is straight drivingwith intermittent gas pedal presses. In FIG. 8A, the longitudinalacceleration is plotted over time, FIG. 8B the slip ratio and FIG. 8Cthe longitudinal force (actual (CarSim) and estimated (SMC ObserverBased)). The results show that the estimated longitudinal forces closelymatch the simulated forces. Also, the estimated forces converge quicklyto the simulated forces.

The longitudinal force model in the small-slip range can be expressed asfollows:

F _(x) =C _(x)·λ, for |λ|<3%

Satisfactory performance of the wheel dynamics based observer in thesmall slip region (|λ|<3%) provides us with an opportunity to adaptivelyestimate the longitudinal stiffness of the tire using an on-lineparameter estimation algorithm. Above equation can be rewritten into astandard parameter identification form as follows:

y(t)=φ^(T)(t)·θ(t)

where y(t)=F_(x) is the system output (from the wheel dynamics basedobserver), θ(t)=C_(x), is the unknown parameter, and φ^(T)(t)=λ is themeasured slip ratio. The unknown parameter θ(t) can be identified inreal-time using parameter identification approach.

The recursive least squares (RLS) algorithm provides a method toiteratively update the unknown parameter at each sampling time tominimize the sum of the squares of the modeling error using the pastdata contained within the regression vector, φ(t). The procedure orsolving the RLS problem is as follows:

Step 0: Initialize the unknown parameter θ(0) and the covariance matrixP(0); set the forgetting factor λ.

Step 1: Measure the system output y(t) and compute the regression vectorφ(t).

Step 2: Calculate the identification error e(t):

e(t)=y(t)−φ^(T)(t)·θ(t−1)

Step 3: Calculate the gain k(t):

k(t)=P(t−1)φ(t)[λ+φ^(T)(t)P(t−1)φ(t)]⁻¹

Step 4: Calculate the covariance matrix:

P(t)=(1−k(t)φ^(T)(t)λ⁻¹ P(t−1)

Step 5: Update the unknown parameter:

θ(t)=θ(t−1)+k(t)e(t)

Step 6: Repeat Steps 1 through 5 for each time step.

In FIGS. 9A through 9D, experimental validation graphs are shown. Theperformance of the RLS based tire longitudinal stiffness estimationalgorithm is evaluated with simulations where the road surface isdesigned to have sudden friction coefficient changes, and the vehiclemaneuver is straight driving with intermittent gas pedal presses. InFIG. 9A, slip ratio (percent) over time is graphed, and in FIG. 9B,tire-road friction coefficient over time is shown. FIG. 9C shows thealgorithm activation signal and FIG. 9D the parameter estimationresults, graphing longitudinal stiffness (C_(x)) for both actual andestimated values. It can be seen that the estimator shows delayedestimation at the first change due to lack of excitation at that time.Once excitation occurs at 2.2 seconds, the estimator updates thelongitudinal stiffness. The results confirms that estimated longitudinalstiffness (broken line) closely matches actual (solid line).

FIGS. 10A and 10B show a schematic block diagram of how the abovefriction estimation may be used in a sensor fusion approach for improvedroad surface classification. As explained above, tire-based inputs oftire ID, pressure and temperature are obtained from a tire-based TPMSSensor Module. The tire wear state and tire load inputs are derived,either directly from tire sensors or indirectly from vehicle basedsensors, and with the tire-based inputs, are used to compute thefriction estimation from the expression: longitudinal stiffness(actual)=longitudinal stiffness (model based) X Friction Factor. Block50 represents a summary of the friction estimation step.

In order to classify wet surfaces into a detailed condition analysis 52,temperature sensors are used to detect ambient air temperature 54 andrain sensors 56 are used to detect moisture in a moisture activatedsystem 56. Both air temperature and moisture sensor inputs with thefriction estimate 22 from the system and method described previously inreference to FIG. 7 are inputs into a detailed road surface classifier58 in the form of a Modified Sensor Fusion Algorithm using principles ofFuzzy logic.

From the Modified Sensor Fusion Algorithm, a Road Surface Type isdetermined. The table in FIG. 10B shows a comparison between basicsurface types and the surface types determined from the Modified SensorFusion Algorithm approach.

The Road Surface Classifier performance is shown graphically in FIGS. 11and 12. The performance of the RLS based Road Surface Classifieralgorithm is evaluated with simulations where the road surface isdesigned to have sudden friction coefficient changes and the vehiclemaneuver is straight driving with intermittent gas pedal presses. InFIG. 11, friction is plotted over time for actual, predicted (withoutadaptation) and predicted (with tire pressure, temperature, wear, loadstate adaptation). Performance of the road surface classifier wasevaluated for a worn tire (2 mm tread) on different road surfaceconditions. Without the wear state adaptation scaling factor, slip slopebased model overestimates the grip/friction level (see black dasheddotted line 62 in FIG. 11). This is due to the fact that, withoutadaptation, the increased longitudinal stiffness of the tire isincorrectly attributed to an increased road surface friction level when,in reality, the increased stiffness is due to a decrease in the tiretread depth (a worn tire having a higher stiffness).

The adaptation model (see line 66) correctly compensates for this effectand estimates the grip level correctly in correlation to actual 64.

FIG. 12 demonstrates the Road Surface Classifier performance graphicallyfor a hot tire (55° C.). In FIG. 12, friction is plotted over time foractual, predicted (without adaptation) and predicted (with tirepressure, temperature, wear, load state adaptation). Performance of theroad surface classifier was evaluated for a worn tire (2 mm tread) ondifferent road surface conditions. Without the temperature stateadaptation scaling factor, slip slope based model overestimates thegrip/friction level (see black dashed dotted line 68 in FIG. 11). Thisis due to the fact that, without adaptation, the decreased longitudinalstiffness of the tire is incorrectly attributed to a decreased roadsurface friction level when, in reality, the decreased stiffness is dueto an increase in the tire temperature (a hotter tire having a lowerstiffness). The adaptation model (see plotted line 70) correctlycompensates for this effect and estimates the grip level correctly incorrelation to actual 72.

It will be appreciated that tire-road friction coefficient informationis of importance for vehicle dynamic control such as yaw stabilitycontrol, braking control, trajectory tracking control and rolloverprevention. Existing tire-road friction coefficient estimationapproaches require certain levels of vehicle longitudinal and/or lateralmotion excitations (e.g. accelerating, decelerating, and steering) tosatisfy the persistence of excitation condition for reliableestimations.

One approach taken in assessing friction is to estimate the longitudinalstiffness, i.e. the incline of the tire force relative to slip at lowslips and from this value distinguish between different surfaceconditions. This method is more commonly known as the “slip-slopemethod” for friction coefficient estimation. Good estimations from thisapproach, however, in the low slip region are unpredictable.

The subject system and method uses adaption parameters in order toachieve a better tire-road friction estimation, including within the lowslip region. Adaption parameters are used which govern tire longitudinalstiffness behavior in the low slip region and include inflationpressure, tread depth, normal loading and temperature. Using only thevalue of slip-slope itself cannot derive a maximum friction coefficientand is, accordingly, a less than satisfactory friction estimationsolution.

The subject system and method utilizes tire-based attached sensorsystems to compensate for dependencies such as pressure, temperature,wear state, tire construction. Consequently, the subject system andmethodology can then isolate/alienate the effect of friction on the tirelongitudinal stiffness. Using a tire attached TPMS sensor in conjunctionwith information from vehicle-based sensors compensates for the variousoperating conditions a tire experiences in real-world driving scenarios.

As a first step and as explained above, a longitudinal stiffnessadaptation model is developed and implemented for generating amodel-based tire longitudinal stiffness prediction under variousoperating conditions a tire experiences. The adaptation model usesscaling factors to account for the effects of load, inflation pressure,temperature, tire wear-state, and tire type (summer/winter/all season)on the tire longitudinal stiffness. The tire construction (tire ID),inflation pressure, and temperature information is available from atire-attached TPMS sensor module. The tire wear state and loadinformation is available directly from tire attached sensors orindirectly from vehicle based sensors (suspension deflection for loadand hub acceleration for wear state).

In parallel with the model-based estimation of longitudinal stiffness,an on-vehicle (real time) estimate of the tire longitudinal stiffness ismade following a three-step estimation procedure:

(1) estimate the longitudinal tire force (using a sliding mode observerthat relies on engine torque and brake torque measurements and wheelspeed measurement available over the CAN bus of the vehicle);

(2) estimate the tire longitudinal slip ratio (using kinematicrelationship);

(3) calculate the longitudinal stiffness (using a recursive least squarealgorithm with a forgetting factor).

Finally, an estimate of the tire road surface condition is made bycomparing the model-based estimate of stiffness to the actual tirelongitudinal stiffness measured on the vehicle. The proportioning factorbetween the model-based estimate and the actual longitudinal stiffnessis a direct measure of the tire road friction coefficient (μ).

It will be noted that the subject system and method develops real-timefriction coefficient estimation algorithms based on slip-slopecalculations for each tire rather than focusing on “average” frictioncoefficient for the vehicle. Accordingly, the subject system and methodprovides information about the individual wheel tire-road frictioncoefficients, a more valuable measurement for active safety systems thanaverage vehicle-based friction measurements.

Variations in the present invention are possible in light of thedescription of it provided herein. While certain representativeembodiments and details have been shown for the purpose of illustratingthe subject invention, it will be apparent to those skilled in this artthat various changes and modifications can be made therein withoutdeparting from the scope of the subject invention. It is, therefore, tobe understood that changes can be made in the particular embodimentsdescribed which will be within the full intended scope of the inventionas defined by the following appended claims.

What is claimed is:
 1. A tire-based system for estimating road surfacefriction comprising: at least one tire mounted to a wheel hub andsupporting a vehicle; model-based longitudinal stiffness estimatingmeans for producing a model-based longitudinal stiffness estimation forthe one tire from tire-based inputs and vehicle-based inputs; actuallongitudinal stiffness estimating means for producing an actuallongitudinal stiffness estimation from vehicle-based inputs; tire roadfriction estimating means for deriving a road friction estimation from acomparative analysis between the actual longitudinal stiffnessestimation and the model-based longitudinal stiffness estimation.
 2. Thesystem of claim 1, wherein the tire-based inputs are at least one inputfrom the group: a measured air cavity pressure of the one tire;tire-specific construction characteristics of the one tire; a measuredtemperature of the one tire.
 3. The system of claim 1, wherein thevehicle-based inputs are at least one input from the group: a measuredwheel speed of the vehicle; a measured wheel torque; a measured hubvertical acceleration; a measured wheel slip ratio.
 4. The system ofclaim 3, wherein further comprising tire wear state estimating means forproducing a wear state estimation for the one tire from the measured hubvertical acceleration.
 5. The system of claim 4, wherein the tire wearstate estimating means operably produces the tire wear state estimationfrom a detected a shift in a vertical mode of the one tire.
 6. Thesystem of claim 3, wherein the model-based longitudinal stiffnessestimating means algorithmically calculates the longitudinal stiffnessestimation from inputs including vehicle load, the measured air cavitypressure of the one tire and the measured temperature of the one tirecompensated by the estimated tire wear state.
 7. The system of claim 6,wherein the actual longitudinal stiffness estimating means comprises alongitudinal force estimation means for generating a longitudinal forceestimation from the measured wheel speed and the measured wheel torque.8. The system of claim 7, wherein the longitudinal force estimationmeans comprises a sliding mode observer model.
 9. The system of claim 8,wherein the actual longitudinal stiffness estimation means calculatesthe actual longitudinal stiffness estimation from the longitudinal forceestimation and the measured wheel slip ratio.
 10. The system of claim 9,wherein the actual longitudinal stiffness estimating means comprises arecursive least square algorithm with forgetting factor.
 11. The systemof claim 1, wherein further comprising a road surface classifieralgorithm operably conducting a road surface type analysis based on theroad friction estimation, an ambient air temperature measurement, and anambient air moisture measurement.
 12. The system of claim 11, whereinthe road surface classifier algorithm comprises a modified sensor fusionalgorithm.
 13. A tire-based method of estimating road surface frictionbased on at least one tire mounted to a wheel hub and supporting avehicle, comprising: generating a model-based longitudinal stiffnessestimation from tire-based parameter inputs from the one tire andvehicle-based parameter inputs; generating an actual longitudinalstiffness estimation from vehicle-based parameter inputs; deriving atire road friction estimation from a comparative analysis between theactual longitudinal stiffness estimation and the model-basedlongitudinal stiffness estimation.
 14. The method of claim 13, whereinfurther comprising: using as the tire-based parameter inputs from theone tire at least one parameter input from the group: measured aircavity pressure of the one tire; tire-specific constructionspecifications of the one tire; temperature of the one tire.
 15. Themethod of claim 14, wherein further comprising: using as thevehicle-based parameter inputs from the vehicle at least one input fromthe group: measured wheel speed of the vehicle; measured wheel torque;measured hub vertical acceleration; measured wheel slip ratio.
 16. Themethod of claim 15, wherein further comprising generating a tire wearstate estimation of the one tire from the measured hub verticalacceleration by detecting a shift in a vertical mode of the one tire.17. The method of claim 16, wherein further comprising generating alongitudinal stiffness estimation from vehicle-based input parametersincluding a vehicle load estimation, the measured air cavity pressure ofthe one tire, and the measured temperature of the one tire compensatedby the wear state estimation of the one tire.
 18. The method of claim17, wherein further comprising making a longitudinal force estimationfrom the measured wheel speed and the measured wheel torque.
 19. Themethod of claim 18, wherein further comprising using a sliding modeobserver model in making the longitudinal force estimation.
 20. Themethod of claim 13, wherein further comprising utilizing a modifiedsensor fusion algorithm to determine a road surface type analysis usingas parameter inputs the road friction estimation, an ambient airtemperature measurement, and an ambient air moisture measurement.